The closed range property for the $\overline{\partial }$-operator on planar domains

A. -K. Gallagher, J. Lebl, K. Ramachandran

Let $\Omega \subset \mathbb{C}$ be an open set. We show that $\overline{\partial }$ has closed range in $L^2(\Omega )$ if and only if the Poincaré-Dirichlet inequality holds. Moreover, we give…